**Zeros Ones Inflated Proportional**

The ZOIP distribution (Zeros Ones Inflated Proportional) is a proportional data distribution inflated with zeros and/or ones, this distribution is defined on the most known proportional data distributions, the beta and simplex distribution, Jørgensen and Barndorff-Nielsen (1991) <doi:10.1016/0047-259X(91)90008-P>, also allows it to have different parameterizations of the beta distribution, Ferrari and Cribari-Neto (2004) <doi:10.1080/0266476042000214501>, Rigby and Stasinopoulos (2005) <doi:10.18637/jss.v023.i07>. The ZOIP distribution has four parameters, two of which correspond to the proportion of zeros and ones, and the other two correspond to the distribution of the proportional data of your choice. The ‘ZOIP’ package allows adjustments of regression models for fixed and mixed effects for proportional data inflated with zeros and/or ones. … **Fuzzy Supervised Learning with Binary Meta-Feature (FSL-BM)**

This paper introduces a novel real-time Fuzzy Supervised Learning with Binary Meta-Feature (FSL-BM) for big data classification task. The study of real-time algorithms addresses several major concerns, which are namely: accuracy, memory consumption, and ability to stretch assumptions and time complexity. Attaining a fast computational model providing fuzzy logic and supervised learning is one of the main challenges in the machine learning. In this research paper, we present FSL-BM algorithm as an efficient solution of supervised learning with fuzzy logic processing using binary meta-feature representation using Hamming Distance and Hash function to relax assumptions. While many studies focused on reducing time complexity and increasing accuracy during the last decade, the novel contribution of this proposed solution comes through integration of Hamming Distance, Hash function, binary meta-features, binary classification to provide real time supervised method. Hash Tables (HT) component gives a fast access to existing indices; and therefore, the generation of new indices in a constant time complexity, which supersedes existing fuzzy supervised algorithms with better or comparable results. To summarize, the main contribution of this technique for real-time Fuzzy Supervised Learning is to represent hypothesis through binary input as meta-feature space and creating the Fuzzy Supervised Hash table to train and validate model. … **Norm**

In linear algebra, functional analysis and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space – save possibly for the zero vector, which is assigned a length of zero. A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors (in addition to the zero vector). A norm must also satisfy certain properties pertaining to scalability and additivity which are given in the formal definition below. A simple example is the 2-dimensional Euclidean space R2 equipped with the Euclidean norm. Elements in this vector space (e.g., (3, 7)) are usually drawn as arrows in a 2-dimensional cartesian coordinate system starting at the origin (0, 0). The Euclidean norm assigns to each vector the length of its arrow. Because of this, the Euclidean norm is often known as the magnitude. A vector space on which a norm is defined is called a normed vector space. Similarly, a vector space with a seminorm is called a seminormed vector space. It is often possible to supply a norm for a given vector space in more than one way. …

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